USCISのHPのLawsで見てみると、
§ Sec. 214.2(f)
(5) Duration of status--
(iv) Preparation for departure
のところで、
An F-1 student who has completed a course of study and any authorized practical training following completion of studies will be allowed an additional 60-day period to prepare for departure from the United States ....
とあります。
私見ですが、「additional」 60-day period とあるので、翌日から、という解釈でいいのではないかと。